Yes, in the context of similar shapes.
The corresponding angles in both cases are the same. With congruent triangles, the lengths of the corresponding sides are also equal.
Their corresponding angles are equal, or the ratio of the lengths of their corresponding sides is the same.
The 3 sides have different lengths
A ratio of corresponding side lengths being proportional means that the lengths of sides from two similar geometric figures have a consistent relationship. For instance, if two triangles are similar, the ratio of the lengths of their corresponding sides is the same across all three pairs of sides. This proportionality allows for the use of scale factors in calculations involving the figures, such as area and perimeter. Thus, if one triangle has sides of length 3, 4, and 5, and the similar triangle has sides of length 6, 8, and 10, the ratio of corresponding sides is 1:2.
Assuming you are already sure that the two objects are, indeed, similar: You measure corresponding lengths of the two objects, and divide.You measure the lengths of a pair of corresponding sides. The scale factor is the ratio of the two measures.
It is a statement about the relationship of the lengths of corresponding sides of some unspecified figures.
It is a statement about the relationship of the lengths of corresponding sides of some unspecified figures.
It is a statement about the relationship of the lengths of corresponding sides of some unspecified figures.
The corresponding angles in both cases are the same. With congruent triangles, the lengths of the corresponding sides are also equal.
Scale factor.
Corresponding sides of similar figures are proportional.
Their corresponding angles are equal, or the ratio of the lengths of their corresponding sides is the same.
They are the same for pairs of corresponding sides.
The 3 sides have different lengths
1:1
Triangles are congruent if the lengths of their corresponding sides as well as the measures of their corresponding angles are the same.
You either show that the corresponding angles are equal or that the lengths of corresponding sides are in the same ratio.